26 citations · 59 across the 27 of their papers we have counts for
42 papers
Positive bisectional curvature, Ricci mass, and the fundamental group
Ved Datar, Vamsi Pritham Pingali, Harish Seshadri
We prove the finiteness of the integral of the top power of the Ricci form on a complete, noncompact Kähler manifold with positive bisectional curvature. This settles a special cas…
Uniqueness for the Kähler-Yang-Mills equations
Vamsi Pritham Pingali, Chengjian Yao
A formula for the -K-energy functional for the Kähler-Yang-Mills (KYM) equations is provided in this paper. Using this formula and Chen's -geodesic equation on the space of K…
The top Yau--Yang conjecture for Kähler manifolds with positive sectional curvature
Ved V. Datar, Vamsi P. Pingali, Harish Seshadri
We prove that the top wedge power of the Ricci form of a complete non-compact Kähler manifold with positive sectional curvature has finite integral. Using a result of Chen-Zhu, an…
Uniformisation of complete Kähler surfaces with positive sectional curvature
Ved Datar, Vamsi Pritham Pingali, Harish Seshadri
We prove that any complete non-compact Kähler surface with positive sectional curvature is biholomorphic to , establishing the two dimensional case of the weaker form…
The complex Monge-Ampere equation and an application to uniformisation of surfaces
Ved Datar, Vamsi Pritham Pingali, Harish Seshadri
We prove that a complete noncompact Kähler surface with positive and bounded sectional curvature is biholomorphic to . This result confirms a special case of Yau's co…
Positivity properties of the vector bundle Monge-Ampère equation
Aashirwad N. Ballal, Vamsi P. Pingali
We study MA-positivity, a notion of positivity relevant to a vector bundle version of the complex Monge--Ampère equation introduced in an earlier work, and show that for rank-two h…
Gravitating vortices and Symplectic Reduction by Stages
L. Álvarez-Cónsul, M. Garcia-Fernandez, O. García-Prada +2
We undertake a novel approach to the existence problem for gravitating vortices on a Riemann surface based on symplectic reduction by stages, which seems to be new in the PDE as we…
Non-abelian symmetric critical gravitating vortices on a sphere
Vamsi Pritham Pingali
We produce examples of solutions to the non-abelian gravitating vortex equations, which are a dimensional reduction of the Käher-Yang-Mills- Higgs equations. These are equations fo…
Criteria for the ampleness of certain vector bundles
Indranil Biswas, Vamsi Pritham Pingali
We prove that certain vector bundles over surfaces are ample if they are so when restricted to divisors, certain numerical criteria hold, and they are semistable (with respect to $…
Obstructions to the existence of solutions of the self-dual Einstein-Maxwell-Higgs equations on a compact surface
Luis Álvarez-Cónsul, Mario Garcia-Fernandez, Oscar García-Prada +2
In this note we present an obstruction to the existence of solutions to the self-dual Einstein-Maxwell-Higgs equations on a compact surface, which depends on the multiplicities of…
The Demailly system for a direct sum of ample line bundles on Riemann surfaces
Vamsi Pritham Pingali
We prove that a system of equations introduced by Demailly (to attack a conjecture of Griffiths) has a smooth solution for a direct sum of ample line bundles on a Riemann surface.…
Stability of SGD: Tightness Analysis and Improved Bounds
Yikai Zhang, Wenjia Zhang, Sammy Bald +3
Stochastic Gradient Descent (SGD) based methods have been widely used for training large-scale machine learning models that also generalize well in practice. Several explanations h…
A note on Demailly's approach towards a conjecture of Griffiths
Vamsi Pritham Pingali
We prove that a "cushioned" Hermitian-Einstein-type equation proposed by Demailly in an approach towards a conjecture of Griffiths on the existence of a Griffiths positively curved…
On an asymptotic characterisation of Griffiths semipositivity
Apoorva Khare, Vamsi Pritham Pingali
We prove that certain possibly non-smooth Hermitian metrics are Griffiths-semipositively curved if and only if they satisfy an asymptotic extension property. This result answers a…
A numerical criterion for generalised Monge-Ampere equations on projective manifolds
Ved V. Datar, Vamsi Pritham Pingali
We prove that generalised Monge-Ampère equations (a family of equations which includes the inverse Hessian equations like the -equation, as well as the Monge-Ampère equation) on…
Gravitating vortices with positive curvature
Mario Garcia-Fernandez, Vamsi Pritham Pingali, Chengjian Yao
We give a complete solution to the existence problem for gravitating vortices with non-negative topological constant . Our first main result builds on previous resul…
The deformed Hermitian Yang-Mills equation on three-folds
Vamsi Pritham Pingali
We prove an existence result for the deformed Hermitian Yang-Mills equation for the full admissible range of the phase parameter, i.e., , on com…
On coupled constant scalar curvature Kähler metrics
Ved V. Datar, Vamsi Pritham Pingali
We provide a moment map interpretation for the coupled Kähler-Einstein equations introduced by Hultgren and Witt Nyström, and in the process introduce a more general system of equa…
Non-uniformly flat affine algebraic hypersurfaces
Vamsi Pingali, Dror Varolin
The relationship between interpolation and separation properties of hypersurfaces in Bargmann-Fock spaces over is not well-understood except for . We present f…
A vector bundle version of the Monge-Ampere equation
Vamsi Pritham Pingali
We introduce a vector bundle version of the complex Monge-Ampere equation motivated by a desire to study stability conditions involving higher Chern forms. We then restrict ourselv…
A characterization of finite vector bundles on Gauduchon astheno-Kahler manifolds
Indranil Biswas, Vamsi Pritham Pingali
A vector bundle E on a projective variety X is called finite if it satisfies a nontrivial polynomial equation with integral coefficients. A theorem of Nori implies that E is finite…
Metric properties of parabolic ample bundles
Indranil Biswas, Vamsi Pritham Pingali
We introduce a notion of admissible Hermitian metrics on parabolic bundles and define positivity properties for the same. We develop Chern-Weil theory for parabolic bundles and pro…
Quillen metrics and perturbed equations
Vamsi Pritham Pingali
We come up with infinite-dimensional prequantum line bundles and moment map interpretations of three different sets of equations - the generalised Monge-Amp`ere equation, the almos…
Existence of coupled Kähler-Einstein metrics using the continuity method
Vamsi Pritham Pingali
In this paper we prove the existence of coupled Kähler-Einstein metrics on complex manifolds whose canonical bundle is ample. These metrics were introduced and their existence in t…